The efficiency of various modelling strategies based on the non-linear representation of Reynolds stress in terms of strain and vorticity rates, is addressed for vortex-shedding flows past a bluff body. Two of these models were successfully modified to cope with highly-strained flows. Further, a novel modelling methodology is proposed, based on zonal coupling of a second-order closure for turbulence, solving the outer core flow region, with a one-equation non-linear model for near-wall flow regions. The merits of each approach are evaluated through comparison of the results with the available experimental data for vortex-shedding flow past a square cylinder at Re=22,000. All the models were found to reproduce fairly well the shedding dynamics, with a common predictive trend; that is, the total fluctuating energy is in good accord with the measurements whereas the turbulent kinetic energy is significantly underestimated. The stress–strain relationships were found to be more dominant with incorporating the cubic stress–strain products forming the anisotropic stress tensor. The novel zonal second-order closure was found to be superior to all other methods. The method was also capable to predict the periodic doubling phenomenon, in accord with direct numerical simulation (DNS) and experiments in which the flow was deliberately forced to two-dimensionality.